In the preceding section, differential equations were given for three types of problems. In order to solve these equations, we need to define boundary and initial conditions. Classical boundary conditions may be considered: imposed displacements or forces for solid mechanics problems and imposed fluid pressures, temperatures, concentrations or fluxes for diffusion and advection-diffusion problems.
However, it may be useful to consider much more complex boundary conditions. For example, in solid mechanics, unilateral contact with friction or interface behaviour is often to be considered.
When coupling phenomena, the question of boundary conditions increases in complexity and has to be discussed.
